The gluing of numerical semigroups

Abstract

If K[V] is the ring of coordinates of a variety V, then V is said to be a complete intersection if its defining ideal is generated by the least possible number of polynomials. In the special case K[V] is taken to be a semigroup ring K[S], the generators of its defining ideal can be chosen to be binomials whose exponents correspond to a presentation of the monoid S (see [41]). In this way the concept of complete intersection translates to finitely generated monoids as those having the least possible number of relations in their minimal presentations.